Link quandles are residually finite

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Link quandles are residually finite. / Bardakov, Valeriy G.; Singh, Mahender; Singh, Manpreet.

In: Monatshefte fur Mathematik, Vol. 191, No. 4, 01.04.2020, p. 679-690.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, VG, Singh, M & Singh, M 2020, 'Link quandles are residually finite', Monatshefte fur Mathematik, vol. 191, no. 4, pp. 679-690. https://doi.org/10.1007/s00605-019-01336-z

APA

Bardakov, V. G., Singh, M., & Singh, M. (2020). Link quandles are residually finite. Monatshefte fur Mathematik, 191(4), 679-690. https://doi.org/10.1007/s00605-019-01336-z

Vancouver

Bardakov VG, Singh M, Singh M. Link quandles are residually finite. Monatshefte fur Mathematik. 2020 Apr 1;191(4):679-690. doi: 10.1007/s00605-019-01336-z

Author

Bardakov, Valeriy G. ; Singh, Mahender ; Singh, Manpreet. / Link quandles are residually finite. In: Monatshefte fur Mathematik. 2020 ; Vol. 191, No. 4. pp. 679-690.

BibTeX

@article{938d7ec1dcdd4c1bb4a963613e4fc210,

title = "Link quandles are residually finite",

abstract = "Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.",

keywords = "Free product, Free quandle, Irreducible 3-manifold, Link quandle, Residually finite quandle, KNOT",

author = "Bardakov, {Valeriy G.} and Mahender Singh and Manpreet Singh",

year = "2020",

month = apr,

day = "1",

doi = "10.1007/s00605-019-01336-z",

language = "English",

volume = "191",

pages = "679--690",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "4",

}

RIS

TY - JOUR

T1 - Link quandles are residually finite

AU - Bardakov, Valeriy G.

AU - Singh, Mahender

AU - Singh, Manpreet

PY - 2020/4/1

Y1 - 2020/4/1

N2 - Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.

AB - Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.

KW - Free product

KW - Free quandle

KW - Irreducible 3-manifold

KW - Link quandle

KW - Residually finite quandle

KW - KNOT

UR - http://www.scopus.com/inward/record.url?scp=85074458192&partnerID=8YFLogxK

U2 - 10.1007/s00605-019-01336-z

DO - 10.1007/s00605-019-01336-z

M3 - Article

AN - SCOPUS:85074458192

VL - 191

SP - 679

EP - 690

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 4

ER -

ID: 22337750